Chern-Simons Modified RPA-Eliashberg Theory of the ν=1/2+1/2 Quantum Hall Bilayer.

The ν=1/2+1/2 quantum Hall bilayer has been previsously modeled using Chern-Simons-RPA-Eliashberg (CSRPAE) theory to describe pairing between the two layers. However, these approaches are troubled by a number of divergences and ambiguities. By using a "modified" RPA approximation to account for mass renormalization, we can work in a limit where the cyclotron frequency is taken to infinity, effectively projecting to a single Landau level.

The superconductivity of SrRuO under c-axis uniaxial stress.

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor SrRuO can be tuned through a single Van Hove point, resulting in strong enhancement of both T and H. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously.

Global Phase Diagram of the Normal State of Twisted Bilayer Graphene.

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well.

s-Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1.

We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length.

Exciton Band Topology in Spontaneous Quantum Anomalous Hall Insulators: Applications to Twisted Bilayer Graphene.

We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite nonzero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature.

Partial Equilibration of the Anti-Pfaffian Edge due to Majorana Disorder.

We consider electrical and thermal equilibration of the edge modes of the anti-Pfaffian quantum Hall state at ν=5/2 due to tunneling of the Majorana edge mode to trapped Majorana zero modes in the bulk. Such tunneling breaks translational invariance and allows scattering between Majorana and other edge modes in such a way that there is a parametric difference between the length scales for equilibration of charge and heat transport between integer and Bose mode, on the one hand, and for thermal equilibration of the Majorana edge mode, on the other hand. We discuss a parameter regime in which this mechanism could explain the recent observation of quantized heat transport [M.

Transport in Bilayer Graphene near Charge Neutrality: Which Scattering Mechanisms Are Important?

Using the semiclassical quantum Boltzmann equation (QBE), we numerically calculate the dc transport properties of bilayer graphene near charge neutrality. We find, in contrast to prior discussions, that phonon scattering is crucial even at temperatures below 40 K. Nonetheless, electron-electron scattering still dominates over phonon collisions allowing a hydrodynamic approach.

Interaction Effects and Charge Quantization in Single-Particle Quantum Dot Emitters.

We discuss a theoretical model of an on-demand single-particle emitter that employs a quantum dot, attached to an integer or fractional quantum Hall edge state. Via an exact mapping of the model onto the spin-boson problem we show that Coulomb interactions between the dot and the chiral quantum Hall edge state, unavoidable in this setting, lead to a destruction of precise charge quantization in the emitted wave packet. Our findings cast doubt on the viability of this setup as a single-particle source of quantized charge pulses.

Theory of the Josephson Junction Laser.

We develop an analytic theory for the recently demonstrated Josephson junction laser [M. C. Cassidy et al.

Strong peak in Tc of Sr2RuO4 under uniaxial pressure.

SrRuO is an unconventional superconductor that has attracted widespread study because of its high purity and the possibility that its superconducting order parameter has odd parity. We study the dependence of its superconductivity on anisotropic strain. Applying uniaxial pressures of up to ~1 gigapascals along a 〈100〉 direction (a axis) of the crystal lattice results in the transition temperature (T) increasing from 1.

Large Chern Number and Edge Currents in Sr2RuO4.

We show from a weak-coupling microscopic calculation that the most favored chiral superconducting order parameter in Sr2RuO4 has a Chern number of |C|=7. The two dominant components of this order parameter are given by sin(3k(x))+isin(3k(y)) and sin(k(x))cos(k(y))+isin(k(y))cos(k(x)) and lie in the same irreducible representation E(u) of the tetragonal point group as the usually assumed gap function, sin(k(x))+isin(k(y)). While the latter gap function leads to C=1, the two former lead to C=-7, which is also allowed for an E_{u} gap function since the tetragonal symmetry only fixes C modulo 4.

Signatures of fractional exclusion statistics in the spectroscopy of quantum Hall droplets.

We show how spectroscopic experiments on a small Laughlin droplet of rotating bosons can directly demonstrate Haldane fractional exclusion statistics of quasihole excitations. The characteristic signatures appear in the single-particle excitation spectrum. We show that the transitions are governed by a "many-body selection rule" which allows one to relate the number of allowed transitions to the number of quasihole states on a finite geometry.

Evaluation of ranks of real space and particle entanglement spectra for large systems.

We devise a way to calculate the dimensions of symmetry sectors appearing in the particle entanglement spectrum (PES) and real space entanglement spectrum (RSES) of multiparticle systems from their real space wave functions. We first note that these ranks in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields equality of the multiplicities in the PES and the RSES.

Breaking of particle-hole symmetry by Landau level mixing in the ν=5/2 quantized Hall state.

We perform numerical studies to determine if the fractional quantum Hall state observed at a filling factor of ν=5/2 is the Moore-Read wave function or its particle-hole conjugate, the so-called anti-Pfaffian. Using a truncated Hilbert space approach we find that, for realistic interactions, including Landau-level mixing, the ground state remains fully polarized and the anti-Pfaffian is strongly favored.

Skyrmions in the Moore-Read state at nu=5/2.

We study charged excitations of the non-Abelian Moore-Read liquid at a filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of nonzero well widths, we find that at a sufficiently low Zeeman energy it is energetically favorable for charge e/4 quasiholes to bind into Skyrmions of charge e/2. We show that Skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations.

Paired composite fermion phase of quantum Hall bilayers at nu=1/2+1/2.

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling nu=1/2+1/2 for intermediate spacing between the layers. We identify the phase as p_(x)+ip_(y) pairing, and construct high accuracy trial wave functions to describe the ground state on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes.

Effect of Landau level mixing on braiding statistics.

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of Abelian and non-Abelian quantum Hall states. While path dependent geometric phases can perturb the Abelian part of the statistics, we find that the non-Abelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.

Switching noise as a probe of statistics in the fractional quantum Hall effect.

We propose an experiment to probe the unconventional quantum statistics of quasiparticles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for backscattering. Thermal fluctuations of the number of quasiparticles enclosed between the two point contacts introduce current noise, which reflects the statistics of the quasiparticles.

Crossover from conserving to lossy transport in circular random-matrix ensembles.

In a quantum dot with three leads, the transmission matrix t12 between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the constraints from the symmetry of S become less stringent and t12 becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t12, which is related to a number of physical quantities.

Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map.

Nonlinear penalties due to intrachannel four-wave mixing (IFWM) in highly dispersed return-to-zero differential-phase-shift-keyed transmission are studied for both symmetric and nonsymmetric dispersion maps. As the dispersion map changes from symmetric to nonsymmetric, the nonlinear amplitude fluctuation overtakes the effect of the nonlinear phase fluctuation and dominates the system's nonlinear performance. The effect of IFWM on the bit error rate is assessed by using the semianalytical method.

Eigenvalue density of correlated complex random Wishart matrices.

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theory to multivariate analysis.

Charge separation of dense two-dimensional electron-hole gases: mechanism for exciton ring pattern formation.

We report on new experiments and theory that unambiguously resolve the recent puzzling observation of large diameter exciton emission halos around a laser excitation spot in two dimensional systems. We find a novel separation of plasmas of opposite charge with emission from the sharp circular boundary between these two regions. This charge separation allows for cooling of initially hot optically generated carriers as they dwell in the charge reservoirs for very long times.